How is math used outside academia?
Help me out, beloved readers. Brainstorm with me.
I want to give actual examples, with fully defined models, where I can explain the data, the purported goal, the underlying assumptions, the actual outputs, the political context, and the reach of each model.
The cool thing about these talks is I don’t need to dumb down the math at all, obviously, so I can be quite detailed in certain respects, but I don’t want to assume my audience knows the context at all, especially the politics of the situation.
So far I have examples from finance, internet advertising, and educational testing. Please tell me if you have some more great examples, I want this talk to be awesome.
The ultimate goal of this project is probably an up-to-date essay, modeled after this one, which you should read. Published in the Notices of the AMS in January 2003, author Mary Poovey explains how mathematical models are used and abused in finance and accounting, how Enron booked future profits as current earnings and how they manipulated the energy market. From the essay:
Thus far the role that mathematics has played in these financial instruments has been as much inspirational as practical: people tend to believe that numbers embody objectivity even when they do not see (or understand) the calculations by which particular numbers are generated. In my final example, mathematical principles are still invisible to the vast majority of investors, but mathematical equations become the prime movers of value. The belief that makes it possible for mathematics to generate value is not simply that numbers are objective but that the market actually obeys mathematical rules. The instruments that embody this belief are futures options or, in their most arcane form, derivatives.
Slightly further on she explains:
In 1973 two economists produced a set of equations, the Black-Scholes equations, that provided the first strictly quantitative instrument for calculating the prices of options in which the determining variable is the volatility of the underlying asset. These equations enabled analysts to standardize the pricing of derivatives in exclusively quantitative terms. From this point it was no longer necessary for traders to evaluate individual stocks by predicting the probable rates of profit, estimating public demand for a particular commodity, or subjectively getting a feel for the market. Instead, a futures trader could engage in trades driven purely by mathematical equations and selected by a software program.
She ends with a bunch of great questions. Mind you, this was in 2003, before the credit crisis:
But what if markets are too complex for mathematical models? What if irrational and completely unprecedented events do occur, and when they do—as we know they do—what if they affect markets in ways that no mathematical model can predict? What if the regularity that all mathematical models assume effaces social and cultural variables that are not subject to mathematical analysis? Or what if the mathematical models traders use to price futures actually influence the future in ways the models cannot predict and the analysts cannot govern? Perhaps these are the only questions that can challenge the financial axis of power, which otherwise threatens to remake everything, including value, over in the image of its own abstractions. Perhaps these are the kinds of questions that mathematicians and humanists, working together, should ask and try to answer.